Previous Lecture

lect15

Next Lecture

lect15, Mon 03/11

Partial differential equations (PDEs)

• Lecture Files

Reading assignment

This week, read NCM sections 11.1-11.3.

References for today’s lecture

NCM sections 11.1 and 11.2.

Outline

• Examples of PDEs
  • Gallery of great PDEs
  • The Poisson equation (steady-state temperature problem)
  • The diffusion equation (time-varying temperature problem)
  • The wave equation (second-order derivatives in time)
• Approximating derivatives by finite differences
• The discrete Laplace operator
• Poisson’s equation; the temperature problem as a PDE
  • In one (space) dimension
  • In two and three dimensions
• The diffusion equation in one dimension
  • Constant coefficients: The heated bar
  • Variable coefficients: The insulated bar
  • A Neumann boundary condition [next time]
  • Animations of matplotlib plots [next time]